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Let $A = (24, 7)$ and $B = (3, 4)$, and let line $p$ be the perpendicular bisector of line segment $\overline{AB}$.  Given that $AB$ meets $p$ at $C = (x, y),$ what is the slope of line $p$?

 Aug 12, 2023
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Note that this problem only asks for the slope of the perpendicular bisector, which does not require knowing the point of intersection between p and AB. To find the slope, first find the slope between the AB.

 

\(m_{\overline{\text{AB}}} = \frac{4-7}{3-24} = \frac{-3}{-21} = \frac{1}{7}\)

 

The relationship between the slope of segment AB and p is the opposite reciprocal. The opposite of 1/7 is -1/7. The reciprocal of -1/7 is -7. Therefore, the slope of p is -7.

 

\(\)

 Aug 13, 2023
edited by The3Mathketeers  Aug 13, 2023

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